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A171245 Reciprocals of the deviation of continued fraction convergents from Pi. 0
7, -790, 12016, -3748629, 1730431227, -3015428685, 8172837003, -34313104062, 114738541304, -620832653094, 2474837590227, -45157370341559, 1726856191927439, -6094457427533473, 12791098836150787, -51642743340781227, 325724575136738920, -1813676066719263909 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Clearly the terms alternate in sign, but the initial choice of sign was arbitrary.

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

The first convergent to Pi, 3, is just over 1/7 too low, so 7 is the first term.

The second convergent, 22/7, is 0.001264+ too high, which is just over 1/790, so -790 is the second term.

PROG

(PARI) for(x=1, 10, t=contfracpnqn(contfrac(Pi, x)); print(truncate(1/(Pi-t[1, 1]/t[2, 1]))))

CROSSREFS

Cf. A001203.

Sequence in context: A162089 A020470 A182282 * A014013 A001467 A342836

Adjacent sequences:  A171242 A171243 A171244 * A171246 A171247 A171248

KEYWORD

sign

AUTHOR

Phil Carmody, Dec 06 2009

EXTENSIONS

More terms from Jinyuan Wang, Aug 23 2021

STATUS

approved

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Last modified October 26 18:30 EDT 2021. Contains 348268 sequences. (Running on oeis4.)